9781118041581

contribution of ($2)(2) ($1)(1) $5. The contribution of process

2 is ($2)(2) ($1)(4) $8 at the unit level. Thus, the LP

formulation is

Maximize:

Subject to:

In the graphic solution, both constraints are binding. The optimal

solution is x 1 50 and x 2 30. Total contribution is $490.

b. Let the supply of labor increase to 120. The new solution is x 1  40

and x 2 40, and total contribution increases to $520. Labor’s shadow

price is 30/10 $3.

c. If the contribution of plywood rises to $3, the new objective function

becomes maximize 7x 1 16x 2. The slope of the objective function

(7/16) no longer lies between the slopes of the input constraints

(1/2 and 1). Therefore, only the labor constraint is binding, and

the firm only uses the second process (i.e., x 1 0). Solving the

binding labor constraint, we have x 2 55. The firm’s maximum

contribution is (16)(55) $880.

11. a. The LP formulation is
    Minimize:
    Subject to:
    ,

where L, M, and D (are all nonnegative integers) and denote the

number of roundtrips to Los Angeles, Miami, and Durham, respectively.

Using a spreadsheet optimizer, one finds the solution, L 3, M 1,

and D 2. The total cost of these six round trips (comprising 20,568

total miles and 12 segments) is $1,975.

b. If the challenge is to fly 25,000 miles, the best solution is: L 4, M2,

and D 0. The total cost of these trips (covering 25,840 miles)

increases to $2,300. Finally, if the requirement is 20,000 miles and

only 10 segments, the optimal solution is: L 3, M2, and D  0

(20,640 miles flown) at a cost of $1,875.

5,200L2,520M1,224D20,000

2L2M2D 12

425L300M200D

2x 1 2x 2   160.

x 1 2x 2   110

5x 1 8x 2

36 Answers to Odd-Numbered Problems

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